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In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the decision-maker. If the decision-maker at time t=0 can commit his/her successors, he/she can choose the policy that is optimal from his/her point of view, and constrain the others to abide by it, although they do not see it as optimal for them. If there is no…
Existing financial NLP benchmarks often rely on labels supplied by outside observers, measuring how language is perceived rather than what speakers have committed to in the market. We introduce StakeBench, an evaluation framework for language understanding grounded in market commitment. StakeBench links 560,876 comments from 2,261 resolved markets to verified position, action, and market-odds records across Polymarke…
This paper studies the continuous-time pre-commitment KMM problem proposed by Klibanoff, Marinacci and Mukerji (2005) in incomplete financial markets, which concerns with the portfolio selection under smooth ambiguity. The decision maker (DM) is uncertain about the dominated priors of the financial market, which are characterized by a second-order distribution (SOD). The KMM model separates risk attitudes and ambigui…
It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical Itô calculus and Taylor expansions, we write the price for out-of-the-money (OTM) and in-the-money (ITM) options as an expansion with respect to the moneyness, where the coefficients are related to the negative (no…
The paper investigates the performance of the European option price when the log asset price follows a rich class of Generalized Tempered Stable (GTS) distribution. The GTS distribution is an alternative to Normal distribution and $α$-stable distribution for modeling asset return and many physical and economic systems. The data used in the option pricing computation comes from fitting the GTS distribution to the unde…
The paper builds a Variance-Gamma (VG) model with five parameters: location ($μ$), symmetry ($δ$), volatility ($σ$), shape ($α$), and scale ($θ$); and studies its application to the pricing of European options. The results of our analysis show that the five-parameter VG model is a stochastic volatility model with a $Γ(α, θ)$ Ornstein-Uhlenbeck type process; the associated Lévy density of the VG model is a KoBoL famil…
We study a multi-agent setting in which brokers transact with an informed trader. Through a sequential Stackelberg-type game, brokers manage trading costs and adverse selection with an informed trader. In particular, supplying liquidity to the informed traders allows the brokers to speculate based on the flow information. They simultaneously attempt to minimize inventory risk and trading costs with the lit market bas…
A physically backed leveraged event position requires real credit: if collateral C receives leverage L, the protocol supplies (L-1)C and uses the combined amount to acquire recognized event exposure. This paper develops a venue-agnostic on-chain credit architecture for that capital layer and an endogenous model of its capital market. It separates traders, Senior Credit LPs, market makers, liquidators, and Liquidation…
Current post-trade clearing systems rely almost exclusively on cash or cash-like collateral, leaving vast reserves of short-term liquidity embedded in trade credit outside formal settlement infrastructures. A key barrier to integrating this liquidity is the near-universal dependence of clearing services on novation, which imposes institutional overhead that restricts accessibility and limits the range of obligations …
Financial markets often appear chaotic, yet ranges are rarely accidental. They emerge from structured interactions between market context and capital conditions. The four-hour timeframe provides a critical lens for observing this equilibrium zone where institutional positioning, leveraged exposure, and liquidity management converge. Funding mechanisms, especially in perpetual futures, act as disciplinary forces that …
Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider the subgame perfect strategies. The later are characterized through an extended Hamilton Jacobi Bellman (HJB) equation. A fixed point iteration is employed to solve the extended HJ…
This research aims to demonstrate a dynamic cointegration-based pairs trading strategy, including an optimal look-back window framework in the cryptocurrency market, and evaluate its return and risk by applying three different scenarios. We employ the Engle-Granger methodology, the Kapetanios-Snell-Shin (KSS) test, and the Johansen test as cointegration tests in different scenarios. We calibrate the mean-reversion sp…
This book, which is in Spanish, provides detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility (as an asset class), real estate, distressed assets, cash, cryptocurrencies, miscella…
Moneyness is where spot sits versus strike — in, at, or out of the money — the first map of option value and of Greek shape.
Time inconsistency is when a plan that is optimal to announce today is not optimal to carry out tomorrow, so promises without commitment are not believed.